Any talk of "equilibrium" and "heat" presumes that we're nearing the point of "herd immunity". But the whole point of "flattening the curve" was to put off the convergence to herd immunity as long as possible, in hopes that new testing and treatment options would open up to "change the game". If you have a network, the fastest way to *disconnect* it into non-communicating sub-networks is to kill the highest degree nodes as quickly as possible. The numerical priority for killing a node should be some non-linear increasing function of that node's *degree*. So both "popular" people, and "popular" events need to be shut down. Stopping *events* with >N people (N perhaps 4?) is important, and we've essentially done that. << But just as important is isolating certain *people* who serially have contact with lots of other people -- e.g., health care workers, grocery store clerks, first responders, etc.
Another analogy is that of "watertight compartments" in ships & submarines. You can arbitrarily set up *barriers* to *partition* (perhaps on a hierarchical basis) people for some period of time into different *cohorts*. Thus, workers would not be allowed to go home at night; everyone is stuck for some period of time with the people they have already been in contact with, and the barriers are impermeable. At 11:58 AM 4/11/2020, Brad Klee wrote:
The Chicago story also caught my eye.
It is sensational and does suggest that super spreaders can have disproportionate effect during bootstrapping.
Later if 30,000 people are infected per day, an anomalous high individual rate shouldn't matter as much (assuming few superspreaders).
Your intuition sounds right to me, and I would add that PDEs are really a better description of the process than an ODE.
Once there is an epicenter, it looks more like a heat equation with sources and sinks.
Presumably if an ODE applies to a gross metric, it could be derived from the PDE.
Epicenters combined with massive transit allows spawning of new epicenters as we have seen, and it probably is fractal in the sense that any city can become an epicenter.
The other sensational story (in my region) was about Mardi Gras, which may have created case 1 in Arkansas and Tennessee.
Yet again the problem is changing one ODE model with too many parameters for another PDE model (or better) with too many parameters.
Epidemiologists might claim to know how to set these parameters, but most of us won't know if our trust is misplaced until after the fact.
We can sit here all day and debate what the best possible theory is, but that speculation is useless unless it generates hypotheses to answer questions:
- Is U.S. at peak infections / day? If not when?
- Is U.S. pandemic duration relatively long? If so, by how much?
When you can't trust the politicians and the talking heads on television, you have to look at the data and make a few assumptions.
I don't know the answers, but at least was able to make a few suggestive plots of available data in the other thread from today.
If you have any of your own estimates, I would be interested to hear.
--Brad